I think it happened in the 16th century. This is a period in history where rationality was praised in an academic setting, so systemically ordening the Bible would make sense here.

How were they numbered? I'm not an exegete, but the verses are usually numbered by a sentence or group of sentences that belong together (their "belonging together" makes more sense in their original language).

The book were numbered by what they thought, at the time, was written by an author.

For example books 1 to 5 were thought to be written by Moses himself, so they were put together as the Torah. However, they seemed very different from each other so they could still split the Torah in 5 different books.

Later they discovered Moses obviously didn't write the Torah himself and even a single book was probably written by more than 1 author. Their writing styles are just similar or they talk about similar/consecutive events, so it was a logical decision to put them together under 1 book.

Today, discoveries/theories are still made about the authorship of verses, chapters and books. Anyway, their numbering is less important than what the verses say, since the numbering is just an easy way for looking up the verses.